Papers › HyperMinHash: MinHash in LogLog space
HyperMinHash: MinHash in LogLog space
Yun William Yu, Griffin M. Weber
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In this extended abstract, we describe and analyze a lossy compression of MinHash from buckets of size O(logn) to buckets of size O(loglogn) by encoding using floating-point notation. This new compressed sketch, which we call HyperMinHash, as we build off a HyperLogLog scaffold, can be used as a drop-in replacement of MinHash. Unlike comparable Jaccard index fingerprinting algorithms in sub-logarithmic space (such as b-bit MinHash), HyperMinHash retains MinHash's features of streaming updates, unions, and cardinality estimation. For a multiplicative approximation error 1+ ϵ on a Jaccard index $ t $, given a random oracle, HyperMinHash needs O(ϵ⁻² ( loglogn + log1/(t ϵ) )) space. HyperMinHash allows estimating Jaccard indices of 0.01 for set cardinalities on the order of 10¹⁹ with relative error of around 10\% using 64KiB of memory; MinHash can only estimate Jaccard indices for cardinalities of 10¹⁰ with the same memory consumption.
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